Dynamics of Klein-Gordon on a compact surface near an homoclinic orbit

Benoît Grébert (1) , Tiphaine Jézéquel (2) , Laurent Thomann (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Equations aux Dérivées Partielles et Physique Mathématique

We consider the Klein-Gordon equation on a Riemannian surface which is globally well-posed in the energy space. This equation has an homoclinic orbit to the origin, and in this paper we study the dynamics close to it. Using a strategy from Groves-Schneider, we show that there are many solutions which stay close to this homocline during all times. We point out that the solutions we construct are not small.

Mots clés: Klein-Gordon equation; wave equation; homoclinic orbit; center manifold

Domaines: Equations aux dérivées partielles [math.AP]

Benoît Grébert, Tiphaine Jézéquel, Laurent Thomann. Dynamics of Klein-Gordon on a compact surface near an homoclinic orbit. Discrete and Continuous Dynamical Systems - Series A, 2014, 34 (9), pp.3485--3510. ⟨hal-00752478v2⟩